Krein factorization of covariance operators of 2-parameter random fields and application to the likelihood ratio

A factorization of the covariance operator (I+R) is derived for the observation process of a 2-parameter random field. This result can be applied to express the determinant term appearing in L.A. Shepp's (1966) expression for the likelihood ratio in terms of the system parameters. This means th...

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Bibliographic Details
Published inIEEE transactions on information theory Vol. 37; no. 1; pp. 53 - 59
Main Authors Leusink, R., Bagchi, A.
Format Journal Article
LanguageEnglish
Published New York, NY IEEE 01.01.1991
Institute of Electrical and Electronics Engineers
Subjects
Applied sciences
Covariance matrix
Exact sciences and technology
Information, signal and communications theory
Kernel
Mathematical methods
Mathematics
Measurement standards
Noise measurement
Signal detection
Signal to noise ratio
Stochastic processes
Telecommunications and information theory
White noise
Random field
Covariance
Mathematical operator
Likelihood ratio
Mathematical method
Factorization
Signal detection
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Summary:A factorization of the covariance operator (I+R) is derived for the observation process of a 2-parameter random field. This result can be applied to express the determinant term appearing in L.A. Shepp's (1966) expression for the likelihood ratio in terms of the system parameters. This means that, in practice, one of the problems in computing the likelihood ratio for random fields is solved. Extensions to the multiparameter case are straightforward. The expression of the determinant of (I+R) in terms of the system parameters may also be used to reexpress the Wong-Zakai correction term (1977).< >
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0018-9448
1557-9654
DOI:10.1109/18.61105